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# Solutions for Chapter 14: Design of Experiments with Several Factors

## Full solutions for Applied Statistics and Probability for Engineers | 5th Edition

ISBN: 9780470053041

Solutions for Chapter 14: Design of Experiments with Several Factors

Solutions for Chapter 14
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##### ISBN: 9780470053041

This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780470053041. Chapter 14: Design of Experiments with Several Factors includes 91 full step-by-step solutions. Since 91 problems in chapter 14: Design of Experiments with Several Factors have been answered, more than 22704 students have viewed full step-by-step solutions from this chapter.

Key Statistics Terms and definitions covered in this textbook
• a-error (or a-risk)

In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

• Analytic study

A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

• Attribute

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

• Average

See Arithmetic mean.

• Average run length, or ARL

The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Causal variable

When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

• Central tendency

The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

• Chi-square (or chi-squared) random variable

A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Covariance matrix

A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

• Cumulative distribution function

For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

• Designed experiment

An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Error of estimation

The difference between an estimated value and the true value.

• Error variance

The variance of an error term or component in a model.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• Gamma random variable

A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

• Gaussian distribution

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications

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